LMFDB - Embedded newform 4033.2.a.d.1.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.875196 q^{2} -0.308395 q^{3} -1.23403 q^{4} -3.82611 q^{5} +0.269906 q^{6} +3.91932 q^{7} +2.83041 q^{8} -2.90489 q^{9} +O(q^{10})$	\(q-0.875196 q^{2} -0.308395 q^{3} -1.23403 q^{4} -3.82611 q^{5} +0.269906 q^{6} +3.91932 q^{7} +2.83041 q^{8} -2.90489 q^{9} +3.34860 q^{10} -1.55195 q^{11} +0.380569 q^{12} +3.48258 q^{13} -3.43017 q^{14} +1.17995 q^{15} -0.00909868 q^{16} -5.16986 q^{17} +2.54235 q^{18} +1.44218 q^{19} +4.72155 q^{20} -1.20870 q^{21} +1.35826 q^{22} -4.94477 q^{23} -0.872884 q^{24} +9.63913 q^{25} -3.04794 q^{26} +1.82104 q^{27} -4.83657 q^{28} -1.94722 q^{29} -1.03269 q^{30} +1.86824 q^{31} -5.65286 q^{32} +0.478614 q^{33} +4.52464 q^{34} -14.9958 q^{35} +3.58473 q^{36} -1.00000 q^{37} -1.26219 q^{38} -1.07401 q^{39} -10.8295 q^{40} +7.17598 q^{41} +1.05785 q^{42} -5.14630 q^{43} +1.91516 q^{44} +11.1144 q^{45} +4.32764 q^{46} +5.32549 q^{47} +0.00280598 q^{48} +8.36108 q^{49} -8.43613 q^{50} +1.59436 q^{51} -4.29762 q^{52} +10.7752 q^{53} -1.59376 q^{54} +5.93794 q^{55} +11.0933 q^{56} -0.444760 q^{57} +1.70420 q^{58} +1.09539 q^{59} -1.45610 q^{60} +6.48770 q^{61} -1.63508 q^{62} -11.3852 q^{63} +4.96556 q^{64} -13.3247 q^{65} -0.418881 q^{66} +6.78990 q^{67} +6.37978 q^{68} +1.52494 q^{69} +13.1242 q^{70} +4.49789 q^{71} -8.22204 q^{72} +2.09804 q^{73} +0.875196 q^{74} -2.97266 q^{75} -1.77969 q^{76} -6.08260 q^{77} +0.939968 q^{78} -4.80550 q^{79} +0.0348126 q^{80} +8.15308 q^{81} -6.28039 q^{82} -0.476349 q^{83} +1.49157 q^{84} +19.7805 q^{85} +4.50402 q^{86} +0.600513 q^{87} -4.39266 q^{88} -13.9578 q^{89} -9.72731 q^{90} +13.6494 q^{91} +6.10201 q^{92} -0.576156 q^{93} -4.66084 q^{94} -5.51793 q^{95} +1.74331 q^{96} +8.48516 q^{97} -7.31758 q^{98} +4.50826 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.875196	−0.618857	−0.309428	−	0.950923i	$-0.600138\pi$
$2$	−0.875196	−0.618857	−0.309428	+	0.950923i	$0.600138\pi$
$3$	−0.308395	−0.178052	−0.0890259	−	0.996029i	$-0.528375\pi$
$3$	−0.308395	−0.178052	−0.0890259	+	0.996029i	$0.528375\pi$
$4$	−1.23403	−0.617016
$5$	−3.82611	−1.71109	−0.855545	−	0.517729i	$-0.826778\pi$
$5$	−3.82611	−1.71109	−0.855545	+	0.517729i	$0.826778\pi$
$6$	0.269906	0.110189
$7$	3.91932	1.48136	0.740682	−	0.671856i	$-0.234502\pi$
$7$	3.91932	1.48136	0.740682	+	0.671856i	$0.234502\pi$
$8$	2.83041	1.00070
$9$	−2.90489	−0.968298
$10$	3.34860	1.05892
$11$	−1.55195	−0.467931	−0.233966	−	0.972245i	$-0.575170\pi$
$11$	−1.55195	−0.467931	−0.233966	+	0.972245i	$0.575170\pi$
$12$	0.380569	0.109861
$13$	3.48258	0.965894	0.482947	−	0.875650i	$-0.339566\pi$
$13$	3.48258	0.965894	0.482947	+	0.875650i	$0.339566\pi$
$14$	−3.43017	−0.916752
$15$	1.17995	0.304662
$16$	−0.00909868	−0.00227467
$17$	−5.16986	−1.25388	−0.626938	−	0.779069i	$-0.715692\pi$
$17$	−5.16986	−1.25388	−0.626938	+	0.779069i	$0.715692\pi$
$18$	2.54235	0.599238
$19$	1.44218	0.330858	0.165429	−	0.986222i	$-0.447099\pi$
$19$	1.44218	0.330858	0.165429	+	0.986222i	$0.447099\pi$
$20$	4.72155	1.05577
$21$	−1.20870	−0.263759
$22$	1.35826	0.289583
$23$	−4.94477	−1.03106	−0.515528	−	0.856873i	$-0.672404\pi$
$23$	−4.94477	−1.03106	−0.515528	+	0.856873i	$0.672404\pi$
$24$	−0.872884	−0.178177
$25$	9.63913	1.92783
$26$	−3.04794	−0.597750
$27$	1.82104	0.350459
$28$	−4.83657	−0.914026
$29$	−1.94722	−0.361590	−0.180795	−	0.983521i	$-0.557867\pi$
$29$	−1.94722	−0.361590	−0.180795	+	0.983521i	$0.557867\pi$
$30$	−1.03269	−0.188542
$31$	1.86824	0.335546	0.167773	−	0.985826i	$-0.446342\pi$
$31$	1.86824	0.335546	0.167773	+	0.985826i	$0.446342\pi$
$32$	−5.65286	−0.999294
$33$	0.478614	0.0833160
$34$	4.52464	0.775970
$35$	−14.9958	−2.53475
$36$	3.58473	0.597455
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−1.26219	−0.204754
$39$	−1.07401	−0.171979
$40$	−10.8295	−1.71229
$41$	7.17598	1.12070	0.560350	−	0.828256i	$-0.310667\pi$
$41$	7.17598	1.12070	0.560350	+	0.828256i	$0.310667\pi$
$42$	1.05785	0.163229
$43$	−5.14630	−0.784804	−0.392402	−	0.919794i	$-0.628356\pi$
$43$	−5.14630	−0.784804	−0.392402	+	0.919794i	$0.628356\pi$
$44$	1.91516	0.288721
$45$	11.1144	1.65684
$46$	4.32764	0.638076
$47$	5.32549	0.776802	0.388401	−	0.921490i	$-0.373028\pi$
$47$	5.32549	0.776802	0.388401	+	0.921490i	$0.373028\pi$
$48$	0.00280598	0.000405009 0
$49$	8.36108	1.19444
$50$	−8.43613	−1.19305
$51$	1.59436	0.223255
$52$	−4.29762	−0.595972
$53$	10.7752	1.48009	0.740045	−	0.672558i	$-0.234804\pi$
$53$	10.7752	1.48009	0.740045	+	0.672558i	$0.234804\pi$
$54$	−1.59376	−0.216884
$55$	5.93794	0.800672
$56$	11.0933	1.48240
$57$	−0.444760	−0.0589099
$58$	1.70420	0.223773
$59$	1.09539	0.142608	0.0713040	−	0.997455i	$-0.477284\pi$
$59$	1.09539	0.142608	0.0713040	+	0.997455i	$0.477284\pi$
$60$	−1.45610	−0.187982
$61$	6.48770	0.830665	0.415332	−	0.909670i	$-0.363665\pi$
$61$	6.48770	0.830665	0.415332	+	0.909670i	$0.363665\pi$
$62$	−1.63508	−0.207655
$63$	−11.3852	−1.43440
$64$	4.96556	0.620694
$65$	−13.3247	−1.65273
$66$	−0.418881	−0.0515607
$67$	6.78990	0.829518	0.414759	−	0.909931i	$-0.363866\pi$
$67$	6.78990	0.829518	0.414759	+	0.909931i	$0.363866\pi$
$68$	6.37978	0.773662
$69$	1.52494	0.183581
$70$	13.1242	1.56865
$71$	4.49789	0.533802	0.266901	−	0.963724i	$-0.414000\pi$
$71$	4.49789	0.533802	0.266901	+	0.963724i	$0.414000\pi$
$72$	−8.22204	−0.968977
$73$	2.09804	0.245557	0.122778	−	0.992434i	$-0.460820\pi$
$73$	2.09804	0.245557	0.122778	+	0.992434i	$0.460820\pi$
$74$	0.875196	0.101739
$75$	−2.97266	−0.343253
$76$	−1.77969	−0.204145
$77$	−6.08260	−0.693177
$78$	0.939968	0.106430
$79$	−4.80550	−0.540661	−0.270331	−	0.962768i	$-0.587133\pi$
$79$	−4.80550	−0.540661	−0.270331	+	0.962768i	$0.587133\pi$
$80$	0.0348126	0.00389216
$81$	8.15308	0.905898
$82$	−6.28039	−0.693553
$83$	−0.476349	−0.0522861	−0.0261431	−	0.999658i	$-0.508323\pi$
$83$	−0.476349	−0.0522861	−0.0261431	+	0.999658i	$0.508323\pi$
$84$	1.49157	0.162744
$85$	19.7805	2.14549
$86$	4.50402	0.485681
$87$	0.600513	0.0643818
$88$	−4.39266	−0.468260
$89$	−13.9578	−1.47952	−0.739762	−	0.672869i	$-0.765062\pi$
$89$	−13.9578	−1.47952	−0.739762	+	0.672869i	$0.765062\pi$
$90$	−9.72731	−1.02535
$91$	13.6494	1.43084
$92$	6.10201	0.636178
$93$	−0.576156	−0.0597446
$94$	−4.66084	−0.480729
$95$	−5.51793	−0.566128
$96$	1.74331	0.177926
$97$	8.48516	0.861538	0.430769	−	0.902462i	$-0.358242\pi$
$97$	8.48516	0.861538	0.430769	+	0.902462i	$0.358242\pi$
$98$	−7.31758	−0.739187
$99$	4.50826	0.453097
$100$	−11.8950	−1.18950
$101$	14.4536	1.43819	0.719094	−	0.694913i	$-0.244557\pi$
$101$	14.4536	1.43819	0.719094	+	0.694913i	$0.244557\pi$
$102$	−1.39537	−0.138163
$103$	−0.790856	−0.0779253	−0.0389627	−	0.999241i	$-0.512405\pi$
$103$	−0.790856	−0.0779253	−0.0389627	+	0.999241i	$0.512405\pi$
$104$	9.85714	0.966572
$105$	4.62461	0.451316
$106$	−9.43042	−0.915963
$107$	−10.6970	−1.03412	−0.517061	−	0.855949i	$-0.672974\pi$
$107$	−10.6970	−1.03412	−0.517061	+	0.855949i	$0.672974\pi$
$108$	−2.24722	−0.216239
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−5.19686	−0.495501
$111$	0.308395	0.0292715
$112$	−0.0356607	−0.00336962
$113$	−16.7219	−1.57306	−0.786532	−	0.617549i	$-0.788126\pi$
$113$	−16.7219	−1.57306	−0.786532	+	0.617549i	$0.788126\pi$
$114$	0.389252	0.0364568
$115$	18.9192	1.76423
$116$	2.40294	0.223107
$117$	−10.1165	−0.935273
$118$	−0.958683	−0.0882539
$119$	−20.2624	−1.85745
$120$	3.33975	0.304876
$121$	−8.59144	−0.781040
$122$	−5.67800	−0.514062
$123$	−2.21303	−0.199543
$124$	−2.30547	−0.207037
$125$	−17.7498	−1.58759
$126$	9.96429	0.887689
$127$	2.20342	0.195521	0.0977607	−	0.995210i	$-0.468832\pi$
$127$	2.20342	0.195521	0.0977607	+	0.995210i	$0.468832\pi$
$128$	6.95989	0.615173
$129$	1.58709	0.139736
$130$	11.6618	1.02280
$131$	−16.7073	−1.45972	−0.729860	−	0.683596i	$-0.760415\pi$
$131$	−16.7073	−1.45972	−0.729860	+	0.683596i	$0.760415\pi$
$132$	−0.590625	−0.0514073
$133$	5.65236	0.490122
$134$	−5.94249	−0.513353
$135$	−6.96749	−0.599666
$136$	−14.6328	−1.25476
$137$	−1.71102	−0.146182	−0.0730911	−	0.997325i	$-0.523286\pi$
$137$	−1.71102	−0.146182	−0.0730911	+	0.997325i	$0.523286\pi$
$138$	−1.33462	−0.113611
$139$	6.41108	0.543781	0.271890	−	0.962328i	$-0.412351\pi$
$139$	6.41108	0.543781	0.271890	+	0.962328i	$0.412351\pi$
$140$	18.5053	1.56398
$141$	−1.64235	−0.138311
$142$	−3.93654	−0.330347
$143$	−5.40480	−0.451972
$144$	0.0264307	0.00220256
$145$	7.45029	0.618713
$146$	−1.83619	−0.151964
$147$	−2.57851	−0.212672
$148$	1.23403	0.101437
$149$	−16.2740	−1.33322	−0.666608	−	0.745409i	$-0.732254\pi$
$149$	−16.2740	−1.33322	−0.666608	+	0.745409i	$0.732254\pi$
$150$	2.60166	0.212424
$151$	13.8604	1.12794	0.563972	−	0.825794i	$-0.309273\pi$
$151$	13.8604	1.12794	0.563972	+	0.825794i	$0.309273\pi$
$152$	4.08196	0.331090
$153$	15.0179	1.21412
$154$	5.32347	0.428977
$155$	−7.14810	−0.574149
$156$	1.32536	0.106114
$157$	−5.13328	−0.409680	−0.204840	−	0.978795i	$-0.565667\pi$
$157$	−5.13328	−0.409680	−0.204840	+	0.978795i	$0.565667\pi$
$158$	4.20575	0.334592
$159$	−3.32302	−0.263532
$160$	21.6285	1.70988
$161$	−19.3802	−1.52737
$162$	−7.13554	−0.560621
$163$	3.29073	0.257750	0.128875	−	0.991661i	$-0.458863\pi$
$163$	3.29073	0.257750	0.128875	+	0.991661i	$0.458863\pi$
$164$	−8.85539	−0.691490
$165$	−1.83123	−0.142561
$166$	0.416899	0.0323576
$167$	3.42615	0.265123	0.132562	−	0.991175i	$-0.457680\pi$
$167$	3.42615	0.265123	0.132562	+	0.991175i	$0.457680\pi$
$168$	−3.42111	−0.263944
$169$	−0.871632	−0.0670486
$170$	−17.3118	−1.32775
$171$	−4.18937	−0.320369
$172$	6.35070	0.484237
$173$	20.5718	1.56405	0.782023	−	0.623250i	$-0.214188\pi$
$173$	20.5718	1.56405	0.782023	+	0.623250i	$0.214188\pi$
$174$	−0.525567	−0.0398431
$175$	37.7789	2.85581
$176$	0.0141207	0.00106439
$177$	−0.337813	−0.0253916
$178$	12.2158	0.915613
$179$	9.99794	0.747281	0.373640	−	0.927574i	$-0.378109\pi$
$179$	9.99794	0.747281	0.373640	+	0.927574i	$0.378109\pi$
$180$	−13.7156	−1.02230
$181$	−26.0771	−1.93830	−0.969148	−	0.246478i	$-0.920727\pi$
$181$	−26.0771	−1.93830	−0.969148	+	0.246478i	$0.920727\pi$
$182$	−11.9459	−0.885486
$183$	−2.00077	−0.147901
$184$	−13.9957	−1.03178
$185$	3.82611	0.281301
$186$	0.504249	0.0369733
$187$	8.02338	0.586728
$188$	−6.57182	−0.479300
$189$	7.13723	0.519157
$190$	4.82927	0.350352
$191$	−0.198842	−0.0143877	−0.00719386	−	0.999974i	$-0.502290\pi$
$191$	−0.198842	−0.0143877	−0.00719386	+	0.999974i	$0.502290\pi$
$192$	−1.53135	−0.110516
$193$	−7.73984	−0.557126	−0.278563	−	0.960418i	$-0.589858\pi$
$193$	−7.73984	−0.557126	−0.278563	+	0.960418i	$0.589858\pi$
$194$	−7.42618	−0.533168
$195$	4.10928	0.294272
$196$	−10.3178	−0.736989
$197$	−6.45600	−0.459971	−0.229986	−	0.973194i	$-0.573868\pi$
$197$	−6.45600	−0.459971	−0.229986	+	0.973194i	$0.573868\pi$
$198$	−3.94561	−0.280402
$199$	−2.54557	−0.180451	−0.0902253	−	0.995921i	$-0.528759\pi$
$199$	−2.54557	−0.180451	−0.0902253	+	0.995921i	$0.528759\pi$
$200$	27.2827	1.92918
$201$	−2.09397	−0.147697
$202$	−12.6497	−0.890032
$203$	−7.63179	−0.535647
$204$	−1.96749	−0.137752
$205$	−27.4561	−1.91762
$206$	0.692153	0.0482246
$207$	14.3640	0.998369
$208$	−0.0316869	−0.00219709
$209$	−2.23819	−0.154819
$210$	−4.04744	−0.279300
$211$	−11.0801	−0.762784	−0.381392	−	0.924413i	$-0.624555\pi$
$211$	−11.0801	−0.762784	−0.381392	+	0.924413i	$0.624555\pi$
$212$	−13.2970	−0.913239
$213$	−1.38713	−0.0950443
$214$	9.36200	0.639973
$215$	19.6903	1.34287
$216$	5.15428	0.350705
$217$	7.32224	0.497066
$218$	0.875196	0.0592757
$219$	−0.647023	−0.0437218
$220$	−7.32762	−0.494028
$221$	−18.0045	−1.21111
$222$	−0.269906	−0.0181149
$223$	−28.1517	−1.88518	−0.942589	−	0.333954i	$-0.891617\pi$
$223$	−28.1517	−1.88518	−0.942589	+	0.333954i	$0.891617\pi$
$224$	−22.1554	−1.48032
$225$	−28.0006	−1.86671
$226$	14.6349	0.973502
$227$	−0.568589	−0.0377386	−0.0188693	−	0.999822i	$-0.506007\pi$
$227$	−0.568589	−0.0377386	−0.0188693	+	0.999822i	$0.506007\pi$
$228$	0.548848	0.0363484
$229$	−20.0063	−1.32205	−0.661027	−	0.750362i	$-0.729879\pi$
$229$	−20.0063	−1.32205	−0.661027	+	0.750362i	$0.729879\pi$
$230$	−16.5580	−1.09181
$231$	1.87584	0.123421
$232$	−5.51144	−0.361844
$233$	−19.7076	−1.29109	−0.645545	−	0.763722i	$-0.723370\pi$
$233$	−19.7076	−1.29109	−0.645545	+	0.763722i	$0.723370\pi$
$234$	8.85394	0.578800
$235$	−20.3759	−1.32918
$236$	−1.35175	−0.0879914
$237$	1.48199	0.0962656
$238$	17.7335	1.14949
$239$	4.41464	0.285559	0.142780	−	0.989755i	$-0.454396\pi$
$239$	4.41464	0.285559	0.142780	+	0.989755i	$0.454396\pi$
$240$	−0.0107360	−0.000693006 0
$241$	2.52885	0.162897	0.0814486	−	0.996678i	$-0.474045\pi$
$241$	2.52885	0.162897	0.0814486	+	0.996678i	$0.474045\pi$
$242$	7.51919	0.483352
$243$	−7.97748	−0.511755
$244$	−8.00603	−0.512534
$245$	−31.9904	−2.04379
$246$	1.93684	0.123488
$247$	5.02250	0.319574
$248$	5.28789	0.335782
$249$	0.146904	0.00930963
$250$	15.5346	0.982493
$251$	−15.6228	−0.986101	−0.493050	−	0.870001i	$-0.664118\pi$
$251$	−15.6228	−0.986101	−0.493050	+	0.870001i	$0.664118\pi$
$252$	14.0497	0.885049
$253$	7.67405	0.482464
$254$	−1.92842	−0.121000
$255$	−6.10019	−0.382009
$256$	−16.0224	−1.00140
$257$	−2.67450	−0.166831	−0.0834153	−	0.996515i	$-0.526583\pi$
$257$	−2.67450	−0.166831	−0.0834153	+	0.996515i	$0.526583\pi$
$258$	−1.38902	−0.0864764
$259$	−3.91932	−0.243535
$260$	16.4432	1.01976
$261$	5.65647	0.350127
$262$	14.6221	0.903358
$263$	1.22587	0.0755902	0.0377951	−	0.999286i	$-0.487967\pi$
$263$	1.22587	0.0755902	0.0377951	+	0.999286i	$0.487967\pi$
$264$	1.35467	0.0833744
$265$	−41.2272	−2.53257
$266$	−4.94692	−0.303315
$267$	4.30451	0.263432
$268$	−8.37895	−0.511826
$269$	8.24595	0.502764	0.251382	−	0.967888i	$-0.419115\pi$
$269$	8.24595	0.502764	0.251382	+	0.967888i	$0.419115\pi$
$270$	6.09792	0.371108
$271$	−4.12255	−0.250427	−0.125213	−	0.992130i	$-0.539962\pi$
$271$	−4.12255	−0.250427	−0.125213	+	0.992130i	$0.539962\pi$
$272$	0.0470389	0.00285215
$273$	−4.20939	−0.254764
$274$	1.49748	0.0904658
$275$	−14.9595	−0.902090
$276$	−1.88183	−0.113273
$277$	−25.3264	−1.52172	−0.760858	−	0.648918i	$-0.775222\pi$
$277$	−25.3264	−1.52172	−0.760858	+	0.648918i	$0.775222\pi$
$278$	−5.61095	−0.336522
$279$	−5.42704	−0.324909
$280$	−42.4442	−2.53652
$281$	2.24273	0.133790	0.0668949	−	0.997760i	$-0.478691\pi$
$281$	2.24273	0.133790	0.0668949	+	0.997760i	$0.478691\pi$
$282$	1.43738	0.0855947
$283$	−2.46292	−0.146405	−0.0732027	−	0.997317i	$-0.523322\pi$
$283$	−2.46292	−0.146405	−0.0732027	+	0.997317i	$0.523322\pi$
$284$	−5.55055	−0.329364
$285$	1.70170	0.100800
$286$	4.73026	0.279706
$287$	28.1250	1.66016
$288$	16.4210	0.967614
$289$	9.72747	0.572204
$290$	−6.52047	−0.382895
$291$	−2.61678	−0.153398
$292$	−2.58905	−0.151512
$293$	−18.6876	−1.09174	−0.545871	−	0.837869i	$-0.683801\pi$
$293$	−18.6876	−1.09174	−0.545871	+	0.837869i	$0.683801\pi$
$294$	2.25670	0.131614
$295$	−4.19109	−0.244015
$296$	−2.83041	−0.164514
$297$	−2.82616	−0.163991
$298$	14.2429	0.825069
$299$	−17.2206	−0.995891
$300$	3.66835	0.211793
$301$	−20.1700	−1.16258
$302$	−12.1306	−0.698036
$303$	−4.45741	−0.256072
$304$	−0.0131219	−0.000752594 0
$305$	−24.8227	−1.42134
$306$	−13.1436	−0.751369
$307$	3.88253	0.221588	0.110794	−	0.993843i	$-0.464661\pi$
$307$	3.88253	0.221588	0.110794	+	0.993843i	$0.464661\pi$
$308$	7.50613	0.427701
$309$	0.243896	0.0138747
$310$	6.25599	0.355316
$311$	16.3655	0.928003	0.464002	−	0.885834i	$-0.346413\pi$
$311$	16.3655	0.928003	0.464002	+	0.885834i	$0.346413\pi$
$312$	−3.03989	−0.172100
$313$	16.4026	0.927132	0.463566	−	0.886062i	$-0.346570\pi$
$313$	16.4026	0.927132	0.463566	+	0.886062i	$0.346570\pi$
$314$	4.49262	0.253533
$315$	43.5611	2.45439
$316$	5.93014	0.333597
$317$	26.0723	1.46437	0.732183	−	0.681108i	$-0.238501\pi$
$317$	26.0723	1.46437	0.732183	+	0.681108i	$0.238501\pi$
$318$	2.90829	0.163089
$319$	3.02200	0.169199
$320$	−18.9988	−1.06206
$321$	3.29891	0.184127
$322$	16.9614	0.945223
$323$	−7.45586	−0.414855
$324$	−10.0612	−0.558954
$325$	33.5691	1.86208
$326$	−2.88003	−0.159510
$327$	0.308395	0.0170543
$328$	20.3110	1.12149
$329$	20.8723	1.15073
$330$	1.60268	0.0882249
$331$	−31.4466	−1.72846	−0.864230	−	0.503097i	$-0.832194\pi$
$331$	−31.4466	−1.72846	−0.864230	+	0.503097i	$0.832194\pi$
$332$	0.587830	0.0322614
$333$	2.90489	0.159187
$334$	−2.99855	−0.164073
$335$	−25.9789	−1.41938
$336$	0.0109976	0.000599966 0
$337$	6.80259	0.370561	0.185280	−	0.982686i	$-0.440681\pi$
$337$	6.80259	0.370561	0.185280	+	0.982686i	$0.440681\pi$
$338$	0.762848	0.0414935
$339$	5.15695	0.280087
$340$	−24.4097	−1.32380
$341$	−2.89942	−0.157013
$342$	3.66652	0.198263
$343$	5.33452	0.288037
$344$	−14.5662	−0.785354
$345$	−5.83459	−0.314124
$346$	−18.0044	−0.967920
$347$	18.7411	1.00607	0.503037	−	0.864265i	$-0.332216\pi$
$347$	18.7411	1.00607	0.503037	+	0.864265i	$0.332216\pi$
$348$	−0.741053	−0.0397246
$349$	17.2179	0.921654	0.460827	−	0.887490i	$-0.347553\pi$
$349$	17.2179	0.921654	0.460827	+	0.887490i	$0.347553\pi$
$350$	−33.0639	−1.76734
$351$	6.34191	0.338506
$352$	8.77297	0.467601
$353$	−0.494249	−0.0263062	−0.0131531	−	0.999913i	$-0.504187\pi$
$353$	−0.494249	−0.0263062	−0.0131531	+	0.999913i	$0.504187\pi$
$354$	0.295653	0.0157138
$355$	−17.2094	−0.913383
$356$	17.2244	0.912890
$357$	6.24880	0.330722
$358$	−8.75015	−0.462460
$359$	−19.6327	−1.03618	−0.518088	−	0.855327i	$-0.673356\pi$
$359$	−19.6327	−1.03618	−0.518088	+	0.855327i	$0.673356\pi$
$360$	31.4584	1.65801
$361$	−16.9201	−0.890533
$362$	22.8226	1.19953
$363$	2.64955	0.139066
$364$	−16.8437	−0.882852
$365$	−8.02733	−0.420169
$366$	1.75107	0.0915297
$367$	27.9043	1.45659	0.728297	−	0.685262i	$-0.240312\pi$
$367$	27.9043	1.45659	0.728297	+	0.685262i	$0.240312\pi$
$368$	0.0449909	0.00234531
$369$	−20.8455	−1.08517
$370$	−3.34860	−0.174085
$371$	42.2315	2.19255
$372$	0.710995	0.0368634
$373$	18.3547	0.950373	0.475186	−	0.879885i	$-0.342381\pi$
$373$	18.3547	0.950373	0.475186	+	0.879885i	$0.342381\pi$
$374$	−7.02203	−0.363100
$375$	5.47395	0.282674
$376$	15.0733	0.777347
$377$	−6.78136	−0.349258
$378$	−6.24647	−0.321284
$379$	−24.6431	−1.26583	−0.632917	−	0.774220i	$-0.718142\pi$
$379$	−24.6431	−1.26583	−0.632917	+	0.774220i	$0.718142\pi$
$380$	6.80931	0.349310
$381$	−0.679521	−0.0348129
$382$	0.174026	0.00890393
$383$	24.3837	1.24595	0.622973	−	0.782243i	$-0.285924\pi$
$383$	24.3837	1.24595	0.622973	+	0.782243i	$0.285924\pi$
$384$	−2.14639	−0.109533
$385$	23.2727	1.18609
$386$	6.77387	0.344781
$387$	14.9495	0.759924
$388$	−10.4710	−0.531583
$389$	−22.7803	−1.15501	−0.577503	−	0.816388i	$-0.695973\pi$
$389$	−22.7803	−1.15501	−0.577503	+	0.816388i	$0.695973\pi$
$390$	−3.59642	−0.182112
$391$	25.5638	1.29282
$392$	23.6653	1.19528
$393$	5.15243	0.259906
$394$	5.65026	0.284656
$395$	18.3864	0.925119
$396$	−5.56333	−0.279568
$397$	−25.9145	−1.30061	−0.650307	−	0.759672i	$-0.725360\pi$
$397$	−25.9145	−1.30061	−0.650307	+	0.759672i	$0.725360\pi$
$398$	2.22787	0.111673
$399$	−1.74316	−0.0872670
$400$	−0.0877034	−0.00438517
$401$	−7.35679	−0.367380	−0.183690	−	0.982984i	$-0.558804\pi$
$401$	−7.35679	−0.367380	−0.183690	+	0.982984i	$0.558804\pi$
$402$	1.83263	0.0914034
$403$	6.50630	0.324102
$404$	−17.8362	−0.887385
$405$	−31.1946	−1.55007
$406$	6.67931	0.331489
$407$	1.55195	0.0769274
$408$	4.51269	0.223411
$409$	−32.2725	−1.59577	−0.797886	−	0.602808i	$-0.794049\pi$
$409$	−32.2725	−1.59577	−0.797886	+	0.602808i	$0.794049\pi$
$410$	24.0295	1.18673
$411$	0.527669	0.0260280
$412$	0.975941	0.0480812
$413$	4.29320	0.211254
$414$	−12.5713	−0.617848
$415$	1.82257	0.0894662
$416$	−19.6865	−0.965212
$417$	−1.97714	−0.0968211
$418$	1.95886	0.0958108
$419$	6.61722	0.323273	0.161636	−	0.986850i	$-0.448323\pi$
$419$	6.61722	0.323273	0.161636	+	0.986850i	$0.448323\pi$
$420$	−5.70692	−0.278469
$421$	3.28784	0.160239	0.0801197	−	0.996785i	$-0.474470\pi$
$421$	3.28784	0.160239	0.0801197	+	0.996785i	$0.474470\pi$
$422$	9.69724	0.472054
$423$	−15.4700	−0.752176
$424$	30.4983	1.48113
$425$	−49.8330	−2.41725
$426$	1.21401	0.0588188
$427$	25.4274	1.23052
$428$	13.2005	0.638070
$429$	1.66681	0.0804744
$430$	−17.2329	−0.831044
$431$	−24.0525	−1.15857	−0.579284	−	0.815126i	$-0.696668\pi$
$431$	−24.0525	−1.15857	−0.579284	+	0.815126i	$0.696668\pi$
$432$	−0.0165690	−0.000797178 0
$433$	−8.35747	−0.401634	−0.200817	−	0.979629i	$-0.564360\pi$
$433$	−8.35747	−0.401634	−0.200817	+	0.979629i	$0.564360\pi$
$434$	−6.40839	−0.307613
$435$	−2.29763	−0.110163
$436$	1.23403	0.0590994
$437$	−7.13124	−0.341134
$438$	0.566272	0.0270575
$439$	12.1719	0.580933	0.290467	−	0.956885i	$-0.406189\pi$
$439$	12.1719	0.580933	0.290467	+	0.956885i	$0.406189\pi$
$440$	16.8068	0.801234
$441$	−24.2880	−1.15657
$442$	15.7574	0.749504
$443$	35.5867	1.69077	0.845387	−	0.534154i	$-0.179370\pi$
$443$	35.5867	1.69077	0.845387	+	0.534154i	$0.179370\pi$
$444$	−0.380569	−0.0180610
$445$	53.4041	2.53160
$446$	24.6383	1.16666
$447$	5.01880	0.237381
$448$	19.4616	0.919475
$449$	5.21696	0.246204	0.123102	−	0.992394i	$-0.460716\pi$
$449$	5.21696	0.246204	0.123102	+	0.992394i	$0.460716\pi$
$450$	24.5060	1.15523
$451$	−11.1368	−0.524411
$452$	20.6354	0.970606
$453$	−4.27447	−0.200832
$454$	0.497627	0.0233548
$455$	−52.2240	−2.44830
$456$	−1.25885	−0.0589512
$457$	−27.8791	−1.30413	−0.652065	−	0.758163i	$-0.726097\pi$
$457$	−27.8791	−1.30413	−0.652065	+	0.758163i	$0.726097\pi$
$458$	17.5094	0.818162
$459$	−9.41451	−0.439432
$460$	−23.3470	−1.08856
$461$	−2.31531	−0.107835	−0.0539173	−	0.998545i	$-0.517171\pi$
$461$	−2.31531	−0.107835	−0.0539173	+	0.998545i	$0.517171\pi$
$462$	−1.64173	−0.0763801
$463$	−11.6097	−0.539549	−0.269774	−	0.962924i	$-0.586949\pi$
$463$	−11.6097	−0.539549	−0.269774	+	0.962924i	$0.586949\pi$
$464$	0.0177172	0.000822499 0
$465$	2.20444	0.102228
$466$	17.2480	0.799000
$467$	−6.63113	−0.306852	−0.153426	−	0.988160i	$-0.549031\pi$
$467$	−6.63113	−0.306852	−0.153426	+	0.988160i	$0.549031\pi$
$468$	12.4841	0.577079
$469$	26.6118	1.22882
$470$	17.8329	0.822571
$471$	1.58307	0.0729442
$472$	3.10041	0.142708
$473$	7.98682	0.367234
$474$	−1.29703	−0.0595746
$475$	13.9013	0.637837
$476$	25.0044	1.14607
$477$	−31.3008	−1.43317
$478$	−3.86367	−0.176720
$479$	11.6963	0.534419	0.267210	−	0.963638i	$-0.413898\pi$
$479$	11.6963	0.534419	0.267210	+	0.963638i	$0.413898\pi$
$480$	−6.67010	−0.304447
$481$	−3.48258	−0.158792
$482$	−2.21323	−0.100810
$483$	5.97673	0.271951
$484$	10.6021	0.481915
$485$	−32.4652	−1.47417
$486$	6.98185	0.316703
$487$	−20.6959	−0.937819	−0.468910	−	0.883246i	$-0.655353\pi$
$487$	−20.6959	−0.937819	−0.468910	+	0.883246i	$0.655353\pi$
$488$	18.3629	0.831247
$489$	−1.01484	−0.0458928
$490$	27.9979	1.26482
$491$	30.8482	1.39216	0.696080	−	0.717964i	$-0.254926\pi$
$491$	30.8482	1.39216	0.696080	+	0.717964i	$0.254926\pi$
$492$	2.73096	0.123121
$493$	10.0669	0.453389
$494$	−4.39567	−0.197771
$495$	−17.2491	−0.775289
$496$	−0.0169985	−0.000763257 0
$497$	17.6287	0.790755
$498$	−0.128569	−0.00576133
$499$	19.2844	0.863289	0.431644	−	0.902044i	$-0.357934\pi$
$499$	19.2844	0.863289	0.431644	+	0.902044i	$0.357934\pi$
$500$	21.9039	0.979571
$501$	−1.05661	−0.0472057
$502$	13.6730	0.610255
$503$	29.1493	1.29970	0.649851	−	0.760062i	$-0.274831\pi$
$503$	29.1493	1.29970	0.649851	+	0.760062i	$0.274831\pi$
$504$	−32.2248	−1.43541
$505$	−55.3011	−2.46087
$506$	−6.71630	−0.298576
$507$	0.268807	0.0119381
$508$	−2.71909	−0.120640
$509$	7.34758	0.325676	0.162838	−	0.986653i	$-0.447935\pi$
$509$	7.34758	0.325676	0.162838	+	0.986653i	$0.447935\pi$
$510$	5.33886	0.236409
$511$	8.22288	0.363759
$512$	0.102940	0.00454933
$513$	2.62626	0.115952
$514$	2.34071	0.103244
$515$	3.02590	0.133337
$516$	−1.95852	−0.0862192
$517$	−8.26491	−0.363490
$518$	3.43017	0.150713
$519$	−6.34423	−0.278481
$520$	−37.7145	−1.65389
$521$	−21.7576	−0.953217	−0.476609	−	0.879116i	$-0.658134\pi$
$521$	−21.7576	−0.953217	−0.476609	+	0.879116i	$0.658134\pi$
$522$	−4.95052	−0.216678
$523$	23.7632	1.03909	0.519546	−	0.854442i	$-0.326101\pi$
$523$	23.7632	1.03909	0.519546	+	0.854442i	$0.326101\pi$
$524$	20.6173	0.900672
$525$	−11.6508	−0.508482
$526$	−1.07287	−0.0467795
$527$	−9.65855	−0.420733
$528$	−0.00435476	−0.000189516 0
$529$	1.45077	0.0630769
$530$	36.0818	1.56730
$531$	−3.18200	−0.138087
$532$	−6.97520	−0.302413
$533$	24.9909	1.08248
$534$	−3.76729	−0.163026
$535$	40.9281	1.76947
$536$	19.2182	0.830100
$537$	−3.08331	−0.133055
$538$	−7.21682	−0.311139
$539$	−12.9760	−0.558916
$540$	8.59811	0.370004
$541$	−0.400662	−0.0172258	−0.00861290	−	0.999963i	$-0.502742\pi$
$541$	−0.400662	−0.0172258	−0.00861290	+	0.999963i	$0.502742\pi$
$542$	3.60804	0.154978
$543$	8.04204	0.345117
$544$	29.2245	1.25299
$545$	3.82611	0.163893
$546$	3.68404	0.157662
$547$	−35.3478	−1.51136	−0.755681	−	0.654940i	$-0.772694\pi$
$547$	−35.3478	−1.51136	−0.755681	+	0.654940i	$0.772694\pi$
$548$	2.11145	0.0901968
$549$	−18.8461	−0.804330
$550$	13.0925	0.558265
$551$	−2.80824	−0.119635
$552$	4.31621	0.183710
$553$	−18.8343	−0.800916
$554$	22.1656	0.941724
$555$	−1.17995	−0.0500862
$556$	−7.91148	−0.335521
$557$	29.1649	1.23575	0.617877	−	0.786274i	$-0.287993\pi$
$557$	29.1649	1.23575	0.617877	+	0.786274i	$0.287993\pi$
$558$	4.74972	0.201072
$559$	−17.9224	−0.758037
$560$	0.136442	0.00576571
$561$	−2.47437	−0.104468
$562$	−1.96282	−0.0827967
$563$	−45.9279	−1.93563	−0.967816	−	0.251660i	$-0.919023\pi$
$563$	−45.9279	−1.93563	−0.967816	+	0.251660i	$0.919023\pi$
$564$	2.02672	0.0853401
$565$	63.9799	2.69165
$566$	2.15554	0.0906040
$567$	31.9545	1.34196
$568$	12.7309	0.534176
$569$	−23.6545	−0.991647	−0.495824	−	0.868423i	$-0.665134\pi$
$569$	−23.6545	−0.991647	−0.495824	+	0.868423i	$0.665134\pi$
$570$	−1.48932	−0.0623808
$571$	−10.8300	−0.453220	−0.226610	−	0.973986i	$-0.572764\pi$
$571$	−10.8300	−0.453220	−0.226610	+	0.973986i	$0.572764\pi$
$572$	6.66970	0.278874
$573$	0.0613218	0.00256176
$574$	−24.6149	−1.02740
$575$	−47.6633	−1.98770
$576$	−14.4244	−0.601017
$577$	−19.1589	−0.797597	−0.398798	−	0.917039i	$-0.630573\pi$
$577$	−19.1589	−0.797597	−0.398798	+	0.917039i	$0.630573\pi$
$578$	−8.51344	−0.354113
$579$	2.38692	0.0991972
$580$	−9.19391	−0.381756
$581$	−1.86697	−0.0774548
$582$	2.29019	0.0949316
$583$	−16.7226	−0.692580
$584$	5.93831	0.245729
$585$	38.7069	1.60034
$586$	16.3553	0.675632
$587$	25.1587	1.03841	0.519206	−	0.854649i	$-0.326228\pi$
$587$	25.1587	1.03841	0.519206	+	0.854649i	$0.326228\pi$
$588$	3.18197	0.131222
$589$	2.69434	0.111018
$590$	3.66803	0.151010
$591$	1.99100	0.0818986
$592$	0.00909868	0.000373954 0
$593$	−18.5324	−0.761034	−0.380517	−	0.924774i	$-0.624254\pi$
$593$	−18.5324	−0.761034	−0.380517	+	0.924774i	$0.624254\pi$
$594$	2.47345	0.101487
$595$	77.5260	3.17826
$596$	20.0826	0.822616
$597$	0.785040	0.0321295
$598$	15.0714	0.616314
$599$	−18.5532	−0.758063	−0.379032	−	0.925384i	$-0.623743\pi$
$599$	−18.5532	−0.758063	−0.379032	+	0.925384i	$0.623743\pi$
$600$	−8.41384	−0.343494
$601$	20.3028	0.828167	0.414083	−	0.910239i	$-0.364102\pi$
$601$	20.3028	0.828167	0.414083	+	0.910239i	$0.364102\pi$
$602$	17.6527	0.719471
$603$	−19.7239	−0.803220
$604$	−17.1042	−0.695960
$605$	32.8718	1.33643
$606$	3.90111	0.158472
$607$	21.3868	0.868064	0.434032	−	0.900897i	$-0.357090\pi$
$607$	21.3868	0.868064	0.434032	+	0.900897i	$0.357090\pi$
$608$	−8.15243	−0.330625
$609$	2.35360	0.0953729
$610$	21.7247	0.879607
$611$	18.5464	0.750309
$612$	−18.5326	−0.749135
$613$	2.32067	0.0937312	0.0468656	−	0.998901i	$-0.485077\pi$
$613$	2.32067	0.0937312	0.0468656	+	0.998901i	$0.485077\pi$
$614$	−3.39797	−0.137131
$615$	8.46731	0.341435
$616$	−17.2163	−0.693663
$617$	−43.7316	−1.76057	−0.880284	−	0.474447i	$-0.842648\pi$
$617$	−43.7316	−1.76057	−0.880284	+	0.474447i	$0.842648\pi$
$618$	−0.213456	−0.00858647
$619$	−44.5186	−1.78935	−0.894676	−	0.446716i	$-0.852594\pi$
$619$	−44.5186	−1.78935	−0.894676	+	0.446716i	$0.852594\pi$
$620$	8.82099	0.354259
$621$	−9.00461	−0.361343
$622$	−14.3230	−0.574301
$623$	−54.7051	−2.19171
$624$	0.00977207	0.000391196 0
$625$	19.7172	0.788687
$626$	−14.3555	−0.573762
$627$	0.690247	0.0275658
$628$	6.33463	0.252779
$629$	5.16986	0.206136
$630$	−38.1245	−1.51892
$631$	11.3550	0.452037	0.226018	−	0.974123i	$-0.427429\pi$
$631$	11.3550	0.452037	0.226018	+	0.974123i	$0.427429\pi$
$632$	−13.6015	−0.541040
$633$	3.41704	0.135815
$634$	−22.8184	−0.906233
$635$	−8.43051	−0.334555
$636$	4.10071	0.162604
$637$	29.1181	1.15370
$638$	−2.64484	−0.104710
$639$	−13.0659	−0.516879
$640$	−26.6293	−1.05262
$641$	2.85949	0.112943	0.0564716	−	0.998404i	$-0.482015\pi$
$641$	2.85949	0.112943	0.0564716	+	0.998404i	$0.482015\pi$
$642$	−2.88719	−0.113948
$643$	30.7986	1.21458	0.607290	−	0.794480i	$-0.292257\pi$
$643$	30.7986	1.21458	0.607290	+	0.794480i	$0.292257\pi$
$644$	23.9157	0.942412
$645$	−6.07239	−0.239100
$646$	6.52534	0.256736
$647$	−34.0416	−1.33831	−0.669156	−	0.743122i	$-0.733344\pi$
$647$	−34.0416	−1.33831	−0.669156	+	0.743122i	$0.733344\pi$
$648$	23.0766	0.906533
$649$	−1.70000	−0.0667307
$650$	−29.3795	−1.15236
$651$	−2.25814	−0.0885035
$652$	−4.06087	−0.159036
$653$	12.4370	0.486698	0.243349	−	0.969939i	$-0.421754\pi$
$653$	12.4370	0.486698	0.243349	+	0.969939i	$0.421754\pi$
$654$	−0.269906	−0.0105541
$655$	63.9239	2.49771
$656$	−0.0652920	−0.00254922
$657$	−6.09457	−0.237772
$658$	−18.2673	−0.712135
$659$	−34.6419	−1.34946	−0.674728	−	0.738067i	$-0.735739\pi$
$659$	−34.6419	−1.34946	−0.674728	+	0.738067i	$0.735739\pi$
$660$	2.25980	0.0879625
$661$	38.9747	1.51594	0.757971	−	0.652289i	$-0.226191\pi$
$661$	38.9747	1.51594	0.757971	+	0.652289i	$0.226191\pi$
$662$	27.5219	1.06967
$663$	5.55248	0.215640
$664$	−1.34826	−0.0523228
$665$	−21.6266	−0.838642
$666$	−2.54235	−0.0985140
$667$	9.62858	0.372820
$668$	−4.22798	−0.163585
$669$	8.68184	0.335659
$670$	22.7366	0.878393
$671$	−10.0686	−0.388694
$672$	6.83260	0.263573
$673$	−15.5014	−0.597537	−0.298768	−	0.954326i	$-0.596576\pi$
$673$	−15.5014	−0.597537	−0.298768	+	0.954326i	$0.596576\pi$
$674$	−5.95360	−0.229324
$675$	17.5532	0.675624
$676$	1.07562	0.0413701
$677$	−9.28503	−0.356853	−0.178426	−	0.983953i	$-0.557101\pi$
$677$	−9.28503	−0.356853	−0.178426	+	0.983953i	$0.557101\pi$
$678$	−4.51334	−0.173334
$679$	33.2561	1.27625
$680$	55.9869	2.14700
$681$	0.175350	0.00671942
$682$	2.53756	0.0971683
$683$	−1.33664	−0.0511452	−0.0255726	−	0.999673i	$-0.508141\pi$
$683$	−1.33664	−0.0511452	−0.0255726	+	0.999673i	$0.508141\pi$
$684$	5.16982	0.197673
$685$	6.54655	0.250131
$686$	−4.66875	−0.178254
$687$	6.16984	0.235394
$688$	0.0468246	0.00178517
$689$	37.5256	1.42961
$690$	5.10641	0.194398
$691$	−45.0754	−1.71475	−0.857374	−	0.514694i	$-0.827906\pi$
$691$	−45.0754	−1.71475	−0.857374	+	0.514694i	$0.827906\pi$
$692$	−25.3863	−0.965041
$693$	17.6693	0.671201
$694$	−16.4021	−0.622615
$695$	−24.5295	−0.930457
$696$	1.69970	0.0644269
$697$	−37.0988	−1.40522
$698$	−15.0691	−0.570372
$699$	6.07773	0.229881
$700$	−46.6203	−1.76208
$701$	40.3581	1.52430	0.762152	−	0.647398i	$-0.224143\pi$
$701$	40.3581	1.52430	0.762152	+	0.647398i	$0.224143\pi$
$702$	−5.55041	−0.209487
$703$	−1.44218	−0.0543928
$704$	−7.70631	−0.290442
$705$	6.28382	0.236662
$706$	0.432565	0.0162798
$707$	56.6483	2.13048
$708$	0.416872	0.0156670
$709$	−11.1952	−0.420443	−0.210221	−	0.977654i	$-0.567418\pi$
$709$	−11.1952	−0.420443	−0.210221	+	0.977654i	$0.567418\pi$
$710$	15.0616	0.565253
$711$	13.9595	0.523521
$712$	−39.5063	−1.48056
$713$	−9.23803	−0.345967
$714$	−5.46892	−0.204669
$715$	20.6794	0.773365
$716$	−12.3378	−0.461084
$717$	−1.36145	−0.0508443
$718$	17.1825	0.641244
$719$	−41.7646	−1.55756	−0.778778	−	0.627300i	$-0.784160\pi$
$719$	−41.7646	−1.55756	−0.778778	+	0.627300i	$0.784160\pi$
$720$	−0.101127	−0.00376877
$721$	−3.09962	−0.115436
$722$	14.8084	0.551112
$723$	−0.779882	−0.0290041
$724$	32.1800	1.19596
$725$	−18.7695	−0.697083
$726$	−2.31888	−0.0860617
$727$	−45.2083	−1.67668	−0.838342	−	0.545145i	$-0.816475\pi$
$727$	−45.2083	−1.67668	−0.838342	+	0.545145i	$0.816475\pi$
$728$	38.6333	1.43184
$729$	−21.9990	−0.814779
$730$	7.02548	0.260025
$731$	26.6057	0.984046
$732$	2.46902	0.0912575
$733$	−33.3137	−1.23047	−0.615235	−	0.788344i	$-0.710939\pi$
$733$	−33.3137	−1.23047	−0.615235	+	0.788344i	$0.710939\pi$
$734$	−24.4217	−0.901423
$735$	9.86568	0.363901
$736$	27.9521	1.03033
$737$	−10.5376	−0.388158
$738$	18.2439	0.671565
$739$	41.1701	1.51447	0.757233	−	0.653145i	$-0.226551\pi$
$739$	41.1701	1.51447	0.757233	+	0.653145i	$0.226551\pi$
$740$	−4.72155	−0.173567
$741$	−1.54891	−0.0569007
$742$	−36.9609	−1.35688
$743$	−0.637553	−0.0233895	−0.0116948	−	0.999932i	$-0.503723\pi$
$743$	−0.637553	−0.0233895	−0.0116948	+	0.999932i	$0.503723\pi$
$744$	−1.63076	−0.0597865
$745$	62.2660	2.28125
$746$	−16.0640	−0.588145
$747$	1.38374	0.0506285
$748$	−9.90111	−0.362021
$749$	−41.9251	−1.53191
$750$	−4.79078	−0.174935
$751$	16.7160	0.609976	0.304988	−	0.952356i	$-0.401348\pi$
$751$	16.7160	0.609976	0.304988	+	0.952356i	$0.401348\pi$
$752$	−0.0484549	−0.00176697
$753$	4.81798	0.175577
$754$	5.93502	0.216141
$755$	−53.0315	−1.93001
$756$	−8.80757	−0.320328
$757$	36.0850	1.31153	0.655766	−	0.754964i	$-0.272346\pi$
$757$	36.0850	1.31153	0.655766	+	0.754964i	$0.272346\pi$
$758$	21.5676	0.783370
$759$	−2.36664	−0.0859035
$760$	−15.6180	−0.566525
$761$	5.68011	0.205904	0.102952	−	0.994686i	$-0.467171\pi$
$761$	5.68011	0.205904	0.102952	+	0.994686i	$0.467171\pi$
$762$	0.594714	0.0215442
$763$	−3.91932	−0.141889
$764$	0.245378	0.00887745
$765$	−57.4601	−2.07748
$766$	−21.3405	−0.771063
$767$	3.81479	0.137744
$768$	4.94121	0.178301
$769$	−12.6894	−0.457592	−0.228796	−	0.973474i	$-0.573479\pi$
$769$	−12.6894	−0.457592	−0.228796	+	0.973474i	$0.573479\pi$
$770$	−20.3682	−0.734018
$771$	0.824801	0.0297045
$772$	9.55121	0.343756
$773$	−13.9177	−0.500586	−0.250293	−	0.968170i	$-0.580527\pi$
$773$	−13.9177	−0.500586	−0.250293	+	0.968170i	$0.580527\pi$
$774$	−13.0837	−0.470284
$775$	18.0082	0.646875
$776$	24.0165	0.862142
$777$	1.20870	0.0433618
$778$	19.9372	0.714784
$779$	10.3490	0.370793
$780$	−5.07098	−0.181570
$781$	−6.98052	−0.249783
$782$	−22.3733	−0.800068
$783$	−3.54597	−0.126722
$784$	−0.0760748	−0.00271696
$785$	19.6405	0.700999
$786$	−4.50939	−0.160844
$787$	46.7109	1.66506	0.832531	−	0.553978i	$-0.186891\pi$
$787$	46.7109	1.66506	0.832531	+	0.553978i	$0.186891\pi$
$788$	7.96692	0.283810
$789$	−0.378051	−0.0134590
$790$	−16.0917	−0.572516
$791$	−65.5385	−2.33028
$792$	12.7602	0.453415
$793$	22.5939	0.802334
$794$	22.6803	0.804894
$795$	12.7142	0.450928
$796$	3.14131	0.111341
$797$	6.99222	0.247677	0.123839	−	0.992302i	$-0.460480\pi$
$797$	6.99222	0.247677	0.123839	+	0.992302i	$0.460480\pi$
$798$	1.52560	0.0540058
$799$	−27.5320	−0.974013
$800$	−54.4887	−1.92646
$801$	40.5459	1.43262
$802$	6.43863	0.227356
$803$	−3.25606	−0.114904
$804$	2.58402	0.0911315
$805$	74.1506	2.61347
$806$	−5.69429	−0.200573
$807$	−2.54301	−0.0895180
$808$	40.9096	1.43920
$809$	29.2265	1.02755	0.513774	−	0.857925i	$-0.328247\pi$
$809$	29.2265	1.02755	0.513774	+	0.857925i	$0.328247\pi$
$810$	27.3014	0.959273
$811$	6.15466	0.216119	0.108060	−	0.994144i	$-0.465536\pi$
$811$	6.15466	0.216119	0.108060	+	0.994144i	$0.465536\pi$
$812$	9.41788	0.330503
$813$	1.27137	0.0445889
$814$	−1.35826	−0.0476071
$815$	−12.5907	−0.441033
$816$	−0.0145066	−0.000507831 0
$817$	−7.42189	−0.259659
$818$	28.2448	0.987555
$819$	−39.6499	−1.38548
$820$	33.8817	1.18320
$821$	27.2293	0.950308	0.475154	−	0.879903i	$-0.342392\pi$
$821$	27.2293	0.950308	0.475154	+	0.879903i	$0.342392\pi$
$822$	−0.461813	−0.0161076
$823$	−11.0565	−0.385404	−0.192702	−	0.981257i	$-0.561725\pi$
$823$	−11.0565	−0.385404	−0.192702	+	0.981257i	$0.561725\pi$
$824$	−2.23845	−0.0779800
$825$	4.61342	0.160619
$826$	−3.75739	−0.130736
$827$	−49.0123	−1.70433	−0.852163	−	0.523277i	$-0.824709\pi$
$827$	−49.0123	−1.70433	−0.852163	+	0.523277i	$0.824709\pi$
$828$	−17.7257	−0.616010
$829$	−24.5697	−0.853340	−0.426670	−	0.904407i	$-0.640313\pi$
$829$	−24.5697	−0.853340	−0.426670	+	0.904407i	$0.640313\pi$
$830$	−1.59510	−0.0553668
$831$	7.81053	0.270944
$832$	17.2929	0.599525
$833$	−43.2256	−1.49768
$834$	1.73039	0.0599184
$835$	−13.1088	−0.453650
$836$	2.76200	0.0955258
$837$	3.40214	0.117595
$838$	−5.79137	−0.200059
$839$	−35.4166	−1.22272	−0.611359	−	0.791354i	$-0.709377\pi$
$839$	−35.4166	−1.22272	−0.611359	+	0.791354i	$0.709377\pi$
$840$	13.0896	0.451633
$841$	−25.2083	−0.869252
$842$	−2.87750	−0.0991652
$843$	−0.691645	−0.0238215
$844$	13.6732	0.470650
$845$	3.33496	0.114726
$846$	13.5393	0.465489
$847$	−33.6726	−1.15701
$848$	−0.0980402	−0.00336672
$849$	0.759551	0.0260677
$850$	43.6136	1.49593
$851$	4.94477	0.169505
$852$	1.71176	0.0586439
$853$	22.6469	0.775416	0.387708	−	0.921782i	$-0.373267\pi$
$853$	22.6469	0.775416	0.387708	+	0.921782i	$0.373267\pi$
$854$	−22.2539	−0.761514
$855$	16.0290	0.548181
$856$	−30.2770	−1.03485
$857$	−46.0384	−1.57264	−0.786321	−	0.617819i	$-0.788017\pi$
$857$	−46.0384	−1.57264	−0.786321	+	0.617819i	$0.788017\pi$
$858$	−1.45879	−0.0498021
$859$	−32.4682	−1.10780	−0.553901	−	0.832583i	$-0.686861\pi$
$859$	−32.4682	−1.10780	−0.553901	+	0.832583i	$0.686861\pi$
$860$	−24.2985	−0.828572
$861$	−8.67359	−0.295595
$862$	21.0506	0.716988
$863$	5.10564	0.173798	0.0868990	−	0.996217i	$-0.472304\pi$
$863$	5.10564	0.173798	0.0868990	+	0.996217i	$0.472304\pi$
$864$	−10.2941	−0.350211
$865$	−78.7100	−2.67622
$866$	7.31442	0.248554
$867$	−2.99990	−0.101882
$868$	−9.03588	−0.306698
$869$	7.45791	0.252992
$870$	2.01088	0.0681751
$871$	23.6464	0.801227
$872$	−2.83041	−0.0958498
$873$	−24.6485	−0.834225
$874$	6.24123	0.211113
$875$	−69.5673	−2.35180
$876$	0.798448	0.0269771
$877$	25.1762	0.850139	0.425069	−	0.905161i	$-0.360250\pi$
$877$	25.1762	0.850139	0.425069	+	0.905161i	$0.360250\pi$
$878$	−10.6528	−0.359515
$879$	5.76316	0.194386
$880$	−0.0540275	−0.00182127
$881$	51.2600	1.72699	0.863497	−	0.504355i	$-0.168270\pi$
$881$	51.2600	1.72699	0.863497	+	0.504355i	$0.168270\pi$
$882$	21.2568	0.715753
$883$	37.0872	1.24808	0.624041	−	0.781391i	$-0.285490\pi$
$883$	37.0872	1.24808	0.624041	+	0.781391i	$0.285490\pi$
$884$	22.2181	0.747275
$885$	1.29251	0.0434473
$886$	−31.1453	−1.04635
$887$	49.3506	1.65703	0.828516	−	0.559966i	$-0.189186\pi$
$887$	49.3506	1.65703	0.828516	+	0.559966i	$0.189186\pi$
$888$	0.872884	0.0292921
$889$	8.63589	0.289639
$890$	−46.7390	−1.56670
$891$	−12.6532	−0.423898
$892$	34.7401	1.16319
$893$	7.68030	0.257012
$894$	−4.39244	−0.146905
$895$	−38.2532	−1.27866
$896$	27.2780	0.911295
$897$	5.31073	0.177320
$898$	−4.56586	−0.152365
$899$	−3.63788	−0.121330
$900$	34.5537	1.15179
$901$	−55.7064	−1.85585
$902$	9.74686	0.324535
$903$	6.22032	0.206999
$904$	−47.3299	−1.57417
$905$	99.7740	3.31660
$906$	3.74100	0.124286
$907$	8.91988	0.296180	0.148090	−	0.988974i	$-0.452688\pi$
$907$	8.91988	0.296180	0.148090	+	0.988974i	$0.452688\pi$
$908$	0.701657	0.0232853
$909$	−41.9862	−1.39259
$910$	45.7062	1.51515
$911$	5.77703	0.191402	0.0957008	−	0.995410i	$-0.469491\pi$
$911$	5.77703	0.191402	0.0957008	+	0.995410i	$0.469491\pi$
$912$	0.00404673	0.000134001 0
$913$	0.739271	0.0244663
$914$	24.3997	0.807070
$915$	7.65517	0.253072
$916$	24.6884	0.815729
$917$	−65.4812	−2.16238
$918$	8.23954	0.271945
$919$	−31.7558	−1.04753	−0.523763	−	0.851864i	$-0.675472\pi$
$919$	−31.7558	−1.04753	−0.523763	+	0.851864i	$0.675472\pi$
$920$	53.5493	1.76547
$921$	−1.19735	−0.0394541
$922$	2.02635	0.0667342
$923$	15.6643	0.515596
$924$	−2.31485	−0.0761530
$925$	−9.63913	−0.316933
$926$	10.1608	0.333903
$927$	2.29735	0.0754549
$928$	11.0074	0.361335
$929$	−24.2333	−0.795070	−0.397535	−	0.917587i	$-0.630134\pi$
$929$	−24.2333	−0.795070	−0.397535	+	0.917587i	$0.630134\pi$
$930$	−1.92931	−0.0632647
$931$	12.0582	0.395191
$932$	24.3199	0.796623
$933$	−5.04704	−0.165233
$934$	5.80354	0.189898
$935$	−30.6984	−1.00394
$936$	−28.6339	−0.935929
$937$	18.6817	0.610304	0.305152	−	0.952304i	$-0.401293\pi$
$937$	18.6817	0.610304	0.305152	+	0.952304i	$0.401293\pi$
$938$	−23.2905	−0.760463
$939$	−5.05848	−0.165077
$940$	25.1445	0.820124
$941$	27.2456	0.888183	0.444091	−	0.895982i	$-0.353527\pi$
$941$	27.2456	0.888183	0.444091	+	0.895982i	$0.353527\pi$
$942$	−1.38550	−0.0451420
$943$	−35.4836	−1.15550
$944$	−0.00996663	−0.000324386 0
$945$	−27.3078	−0.888324
$946$	−6.99003	−0.227265
$947$	36.6487	1.19092	0.595461	−	0.803384i	$-0.296969\pi$
$947$	36.6487	1.19092	0.595461	+	0.803384i	$0.296969\pi$
$948$	−1.82882	−0.0593975
$949$	7.30658	0.237182
$950$	−12.1664	−0.394730
$951$	−8.04056	−0.260733
$952$	−57.3508	−1.85875
$953$	−29.4079	−0.952615	−0.476308	−	0.879279i	$-0.658025\pi$
$953$	−29.4079	−0.952615	−0.476308	+	0.879279i	$0.658025\pi$
$954$	27.3944	0.886925
$955$	0.760792	0.0246187
$956$	−5.44781	−0.176195
$957$	−0.931968	−0.0301263
$958$	−10.2366	−0.330729
$959$	−6.70603	−0.216549
$960$	5.85912	0.189102
$961$	−27.5097	−0.887409
$962$	3.04794	0.0982695
$963$	31.0737	1.00134
$964$	−3.12068	−0.100510
$965$	29.6135	0.953292
$966$	−5.23081	−0.168299
$967$	−25.2202	−0.811028	−0.405514	−	0.914089i	$-0.632907\pi$
$967$	−25.2202	−0.811028	−0.405514	+	0.914089i	$0.632907\pi$
$968$	−24.3173	−0.781588
$969$	2.29935	0.0738657
$970$	28.4134	0.912299
$971$	−9.75065	−0.312913	−0.156457	−	0.987685i	$-0.550007\pi$
$971$	−9.75065	−0.312913	−0.156457	+	0.987685i	$0.550007\pi$
$972$	9.84447	0.315761
$973$	25.1271	0.805537
$974$	18.1129	0.580376
$975$	−10.3525	−0.331546
$976$	−0.0590295	−0.00188949
$977$	26.1740	0.837379	0.418690	−	0.908129i	$-0.362490\pi$
$977$	26.1740	0.837379	0.418690	+	0.908129i	$0.362490\pi$
$978$	0.888186	0.0284011
$979$	21.6618	0.692315
$980$	39.4772	1.26105
$981$	2.90489	0.0927461
$982$	−26.9982	−0.861548
$983$	−36.6803	−1.16992	−0.584960	−	0.811062i	$-0.698890\pi$
$983$	−36.6803	−1.16992	−0.584960	+	0.811062i	$0.698890\pi$
$984$	−6.26380	−0.199683
$985$	24.7014	0.787052
$986$	−8.81049	−0.280583
$987$	−6.43690	−0.204889
$988$	−6.19793	−0.197182
$989$	25.4473	0.809177
$990$	15.0963	0.479793
$991$	31.8611	1.01210	0.506051	−	0.862503i	$-0.331105\pi$
$991$	31.8611	1.01210	0.506051	+	0.862503i	$0.331105\pi$
$992$	−10.5609	−0.335309
$993$	9.69795	0.307755
$994$	−15.4286	−0.489364
$995$	9.73963	0.308767
$996$	−0.181284	−0.00574419
$997$	−12.0090	−0.380328	−0.190164	−	0.981752i	$-0.560902\pi$
$997$	−12.0090	−0.380328	−0.190164	+	0.981752i	$0.560902\pi$
$998$	−16.8776	−0.534252
$999$	−1.82104	−0.0576151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.32	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.32	✓	79	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-0.875196 q^{2} -0.308395 q^{3} -1.23403 q^{4} -3.82611 q^{5} +0.269906 q^{6} +3.91932 q^{7} +2.83041 q^{8} -2.90489 q^{9} +O(q^{10})\)	\(q-0.875196 q^{2} -0.308395 q^{3} -1.23403 q^{4} -3.82611 q^{5} +0.269906 q^{6} +3.91932 q^{7} +2.83041 q^{8} -2.90489 q^{9} +3.34860 q^{10} -1.55195 q^{11} +0.380569 q^{12} +3.48258 q^{13} -3.43017 q^{14} +1.17995 q^{15} -0.00909868 q^{16} -5.16986 q^{17} +2.54235 q^{18} +1.44218 q^{19} +4.72155 q^{20} -1.20870 q^{21} +1.35826 q^{22} -4.94477 q^{23} -0.872884 q^{24} +9.63913 q^{25} -3.04794 q^{26} +1.82104 q^{27} -4.83657 q^{28} -1.94722 q^{29} -1.03269 q^{30} +1.86824 q^{31} -5.65286 q^{32} +0.478614 q^{33} +4.52464 q^{34} -14.9958 q^{35} +3.58473 q^{36} -1.00000 q^{37} -1.26219 q^{38} -1.07401 q^{39} -10.8295 q^{40} +7.17598 q^{41} +1.05785 q^{42} -5.14630 q^{43} +1.91516 q^{44} +11.1144 q^{45} +4.32764 q^{46} +5.32549 q^{47} +0.00280598 q^{48} +8.36108 q^{49} -8.43613 q^{50} +1.59436 q^{51} -4.29762 q^{52} +10.7752 q^{53} -1.59376 q^{54} +5.93794 q^{55} +11.0933 q^{56} -0.444760 q^{57} +1.70420 q^{58} +1.09539 q^{59} -1.45610 q^{60} +6.48770 q^{61} -1.63508 q^{62} -11.3852 q^{63} +4.96556 q^{64} -13.3247 q^{65} -0.418881 q^{66} +6.78990 q^{67} +6.37978 q^{68} +1.52494 q^{69} +13.1242 q^{70} +4.49789 q^{71} -8.22204 q^{72} +2.09804 q^{73} +0.875196 q^{74} -2.97266 q^{75} -1.77969 q^{76} -6.08260 q^{77} +0.939968 q^{78} -4.80550 q^{79} +0.0348126 q^{80} +8.15308 q^{81} -6.28039 q^{82} -0.476349 q^{83} +1.49157 q^{84} +19.7805 q^{85} +4.50402 q^{86} +0.600513 q^{87} -4.39266 q^{88} -13.9578 q^{89} -9.72731 q^{90} +13.6494 q^{91} +6.10201 q^{92} -0.576156 q^{93} -4.66084 q^{94} -5.51793 q^{95} +1.74331 q^{96} +8.48516 q^{97} -7.31758 q^{98} +4.50826 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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